The 42-year-old told players: "I will do everything to find out who it is," the Bild reported, adding "whoever it is, I will throw them out."
"He will never play for me again," he said. "It doesn't matter who it is, heads will roll."
The threat came in a team talk at their hotel before Saturday's 3-0 away victory over Dortmund.
The tabloid published leaked details of the Spanish coach's strategy against their title rivals before the clash on Saturday afternoon.
It included playing high balls over Dortmund's defence and switching play quickly to undo the back four. He also warned his players to watch out for the Dortmund counterattack.
Bayern chairman Karl-Heinz Rummenigge told the Sky90 talk show he supported the coach's manhunt. "We won't pull any NSA stuff to find them, but I can only advise whoever it is to turn themselves in soon, or they'll have a serious problem, and not just with Pep Guardiola,” he said.
"The coach does part of his training in secret – obviously he's not going to like something like this happening," Rummenigge said.
Asked about Guardiola's "fastidious" leadership style, Rummenigge told Sky90 the coach was "a fanatic…he is unbelievably meticulous."
"He has an unbelievably clear perception of football," the team boss said. "When the players can't put that into play, he gets furious," he added.
The club is keen to get rid of the commotion surrounding the issue of Guardiola's mole threats, news agency DPA reported.
It will be "very much played down," the team's media director Markus Hörwick said.
The news comes as the European Champions celebrate a 38-match winning streak.
On Monday, meanwhile, Rummenigge ruled out bidding for superstar Lionel Messi, who has a buyout clause worth €250 million in his Barcelona contract.
"We are talking about simply absurd figures, a transfer fee that is even higher than what we spent on Javi Martinez. We won't go there," Rummenigge told German Sky Sports.
"Barcelona's president Sandro Rosell is an old friend and I know they would never sell Messi. He is a saint at Barcelona. And I think it would be in Messi's best interest to stay at Barcelona. He fits in perfectly there,” he said.